The Wave Function of Our World: How Does It Emerge?

[jaydnul]

Particles have a wave function, and when measured, they choose one specific eigenvalue to "collapse" to. Is all of the classical stuff we experience in our world then in a collapsed state? For instance, are the particles in the table in front of me at a specific eigenvalue of their wave functions? Or is my body just now included in the non-collapsed quantum wave function with the table?

P.S. I use the word collapse cautiously. I realize this could imply a certain interpretation of the measurement problem, but that is not my aim.

 

[PeroK]

You have misunderstood the concept of a wave function. When some observable is measured, the wave function of a particle changes to an eigenfunction of the operator that represents the observable.

The eigenvalue is the result of the measurement.

 

[Nugatory]

Particles have a wave function, and when measured, they choose one specific eigenvalue to "collapse" to. Is all of the classical stuff we experience in our world then in a collapsed state? For instance, are the particles in the table in front of me at a specific eigenvalue of their wave functions? Or is my body just now included in the non-collapsed quantum wave function with the table?

I've recommended this book so many times that I'm beginning to think I should get a commission on the sales... But if you can get hold of a copy of David Lindley's "Where does the weirdness go?", give it a try. It's a pretty good layman-friendly treatment of how our world emerges from the quantum world.

 

[jaydnul]

You have misunderstood the concept of a wave function. When some observable is measured, the wave function of a particle changes to an eigenfunction of the operator that represents the observable.

The eigenvalue is the result of the measurement.

Sorry I mixed up the terminology.

I've recommended this book so many times that I'm beginning to think I should get a commission on the sales... But if you can get hold of a copy of David Lindley's "Where does the weirdness go?", give it a try. It's a pretty good layman-friendly treatment of how our world emerges from the quantum world.

I'll check it out. I feel like my question is actually much simpler though. I'm not looking for the reason quantum effects don't really manifest in the macroscopic, I'm just curious if the matter we experience everyday is mostly assuming a single value for position, momentum, energy, etc.(whether or not those values display quantum probabilisitc effects or just classical effects)?

 

[stevendaryl]

I'll check it out. I feel like my question is actually much simpler though. I'm not looking for the reason quantum effects don't really manifest in the macroscopic, I'm just curious if the matter we experience everyday is mostly assuming a single value for position, momentum, energy, etc.(whether or not those values display quantum probabilisitc effects or just classical effects)?

The objects we encounter in our everday experience--tables, chairs, etc.--are composed of many, many particles. While for a single particle, it's not possible to have precise values for both position and momentum, when we interact with macroscopic objects, we are dealing with averages over many, many particles. The uncertainty principle has a negligible effect on our ability to know these average quantities. So in that sense, it's not too surprising that macroscopic objects behave approximately classically.

There is a second level of mystery about macroscopic objects, though. In everyday experience, we never observe macroscopic objects to be in a superposition of macroscopically distinguishable states. A coin lying on a table is either heads or tails, and never in a superposition of the two. There isn't complete consensus about the best way to explain that, but a "minimalist" explanation (in the sense that it makes no new assumptions beyond basic QM) is decoherence. Without getting into the details of that, I can motivate why we never observe macroscopic superpositions this way: Ask yourself what it would mean to observe a macroscopic superposition. Let's get people out of the picture, to avoid discussions of consciousness and wave function collapse, and ask a more engineering type question: How would you make a device that observes a coin and prints out "heads" if it is heads-up, "tails" if it is tails-up, and "neither" if it is in a superposition? The answer is that there is no way to make such a device.

 

[mike1000]

There is a second level of mystery about macroscopic objects, though. In everyday experience, we never observe macroscopic objects to be in a superposition of macroscopically distinguishable states. A coin lying on a table is either heads or tails, and never in a superposition of the two. There isn't complete consensus about the best way to explain that, but a "minimalist" explanation (in the sense that it makes no new assumptions beyond basic QM) is decoherence. Without getting into the details of that, I can motivate why we never observe macroscopic superpositions this way: Ask yourself what it would mean to observe a macroscopic superposition. Let's get people out of the picture, to avoid discussions of consciousness and wave function collapse, and ask a more engineering type question: How would you make a device that observes a coin and prints out "heads" if it is heads-up, "tails" if it is tails-up, and "neither" if it is in a superposition? The answer is that there is no way to make such a device.

When the coin is flipping in the air would that be considered as it is in the superposition of two states?

 

[durant35]

Sorry I mixed up the terminology.
I'll check it out. I feel like my question is actually much simpler though. I'm not looking for the reason quantum effects don't really manifest in the macroscopic, I'm just curious if the matter we experience everyday is mostly assuming a single value for position, momentum, energy, etc.(whether or not those values display quantum probabilisitc effects or just classical effects)?

If you assume that decoherence causes collapse, then - yeah, decoherence acts almost instanteneously and collapse comes with it, so every so often on tiny, tiny timescales macroscopic objects collapse from a small superposition to something close to a precise value of an observable (in this case - the position).

 

[PeroK]

If you assume that decoherence causes collapse, then - yeah, decoherence acts almost instanteneously and collapse comes with it, so every so often on tiny, tiny timescales macroscopic objects collapse from a small superposition to something close to a precise value of an observable (in this case - the position).

That makes no sense to me.

 

[durant35]

That makes no sense to me.

Because...?

 

[PeroK]

Because...?

it makes no sense.

 

[Nugatory]

When the coin is flipping in the air would that be considered as it is in the superposition of two states?

No.
(We did have a fairly recent thread about how coin spinning in freefall can be used as an analogy for quantum contextuality. The paper referenced in that thread is wel worth reading - but never forget that an analogy is not the real thing!)

 

[PeterDonis]

When the coin is flipping in the air would that be considered as it is in the superposition of two states?

No. But if you want to consider the coin's continuous motion, instead of just its state at the end of a flip (which is what stevendaryl was doing), then its classical state space contains more than just two states. But it's still a classical state space--you can't observe the coin to be in a superposition of two different states in that state space.

 

[stevendaryl]

If you assume that decoherence causes collapse, then - yeah, decoherence acts almost instanteneously and collapse comes with it, so every so often on tiny, tiny timescales macroscopic objects collapse from a small superposition to something close to a precise value of an observable (in this case - the position).

Decoherence doesn't actually cause collapse of the wave function, but instead makes superpositions unobservable.

A lot of people say that the idea of the wave function of the universe doesn't make sense, but to me, it helps to understand conceptually what's going on with decoherence. Suppose you prepare a particle to be in a superposition of states corresponding to two different spatial locations. That means that the particle is described by the pure state $\alpha |\psi_1\rangle + \beta |\psi_2\rangle$ where let's suppose $|\psi_1\rangle$ is the state in which the particle is most likely to be at one location, $x_1$, and $|\psi_2\rangle$ is the state in which the particle is most likely to be at a macroscopically distant location, $x_2$. Let $|\Psi_0\rangle$ be the state of the entire rest of the universe. So the total wavefunction for the universe would be the state $|\Psi_0\rangle \otimes (\alpha |\psi_1\rangle + \beta |\psi_2\rangle)$. Now, suppose that there is photographic paper spread across the region from $x_1$ to $x_2$ so that the particle interacting with the paper produces a dark spot on the paper (small, but visible to the naked eye). Then the particle interacting with the paper will result in a transition of the form:

$|\Psi_0\rangle \otimes (\alpha |\psi_1\rangle + \beta |\psi_2\rangle) \Longrightarrow \alpha |\Psi_1\rangle + \beta |\Psi_2 \rangle$

where $|\Psi_1\rangle$ is a state in which the photographic paper now has a dark spot at location $x_1$ and $|\Psi_2\rangle$ is a state in which the photographic paper has a dark spot at location $x_2$.

It isn't that the position of the particle has become more definite; it's that the multi-valuedness of the particle's position has "infected" the rest of the universe, to make it multi-valued, as well. In the language of the Many-Worlds Interpretation, the world has "split" into a world in which the particle is at $x_1$ and a world in which the particle is at $x_2$. But you don't have to accept MWI to agree that the interaction between particle and the rest of the world will cause the multi-valuedness to spread beyond just the particle. The two possibilities $|\Psi_1\rangle$ and $|\Psi_2\rangle$ will each evolve independent of each other's existence, so for each possibility, it's as if the other possibility didn't exist.

 

[durant35]

it makes no sense.

How not? Decoherence for macroscopic objects happens in tiny fragments of time. Each time the wavefunction decouples, we can invoke a collapse interpretation where measurement chooses one result from the elements of the superposition. (the elements of the superposition don't interfere with each other + [collapse interpretation] one result is randomly chosen)

Since decoherence occurs continuosly and on such short timescales if we invoke collapse as a end result of decoherence it would happen in a instant in which decoherence ends FAPP, then the process happens again etc.

If you wish to critique this or suggest that something is wrong with my logic and that I need to learn something more, feel free to do so, but with arguments and not with "it doesn't make sense - period".

 

[durant35]

Decoherence doesn't actually cause collapse of the wave function, but instead makes superpositions unobservable.

Well, I think that depends on one's favourite interpretation, it is certain that decoherence causes apparent collapse but you/me are free to assume that real collapse happens when measurement happens, or when the system gets entangled with many degrees of freedom.

Anyway, great post of yours in the context of understanding what happens with decoherence per se. Appreciated.

 

[PeroK]

How not? Decoherence for macroscopic objects happens in tiny fragments of time. Each time the wavefunction decouples, we can invoke a collapse interpretation where measurement chooses one result from the elements of the superposition. (the elements of the superposition don't interfere with each other + [collapse interpretation] one result is randomly chosen)

Since decoherence occurs continuosly and on such short timescales if we invoke collapse as a end result of decoherence it would happen in a instant in which decoherence ends FAPP, then the process happens again etc.

If you wish to critique this or suggest that something is wrong with my logic and that I need to learn something more, feel free to do so, but with arguments and not with "it doesn't make sense - period".

That's a coherent expansion of your earlier post, of which I could make no sense.

My only critique is simply to say that I have no idea how, in QM terms, you would measure the position of a table. Or measure any observable for that matter.

 

[durant35]

That's a coherent expansion of your earlier post, of which I could make no sense.

My only critique is simply to say that I have no idea how, in QM terms, you would measure the position of a table. Or measure any observable for that matter.

Yup, that's fair, I admit I wasn't very coherent in my previous post.

Well, tables are made of many atoms, each atom has its own position so that's the beginning for this way of thinking..

 

[jaydnul]

Decoherence doesn't actually cause collapse of the wave function, but instead makes superpositions unobservable.

A lot of people say that the idea of the wave function of the universe doesn't make sense, but to me, it helps to understand conceptually what's going on with decoherence. Suppose you prepare a particle to be in a superposition of states corresponding to two different spatial locations. That means that the particle is described by the pure state $\alpha |\psi_1\rangle + \beta |\psi_2\rangle$ where let's suppose $|\psi_1\rangle$ is the state in which the particle is most likely to be at one location, $x_1$, and $|\psi_2\rangle$ is the state in which the particle is most likely to be at a macroscopically distant location, $x_2$. Let $|\Psi_0\rangle$ be the state of the entire rest of the universe. So the total wavefunction for the universe would be the state $|\Psi_0\rangle \otimes (\alpha |\psi_1\rangle + \beta |\psi_2\rangle)$. Now, suppose that there is photographic paper spread across the region from $x_1$ to $x_2$ so that the particle interacting with the paper produces a dark spot on the paper (small, but visible to the naked eye). Then the particle interacting with the paper will result in a transition of the form:

$|\Psi_0\rangle \otimes (\alpha |\psi_1\rangle + \beta |\psi_2\rangle) \Longrightarrow \alpha |\Psi_1\rangle + \beta |\Psi_2 \rangle$

where $|\Psi_1\rangle$ is a state in which the photographic paper now has a dark spot at location $x_1$ and $|\Psi_2\rangle$ is a state in which the photographic paper has a dark spot at location $x_2$.

It isn't that the position of the particle has become more definite; it's that the multi-valuedness of the particle's position has "infected" the rest of the universe, to make it multi-valued, as well. In the language of the Many-Worlds Interpretation, the world has "split" into a world in which the particle is at $x_1$ and a world in which the particle is at $x_2$. But you don't have to accept MWI to agree that the interaction between particle and the rest of the world will cause the multi-valuedness to spread beyond just the particle. The two possibilities $|\Psi_1\rangle$ and $|\Psi_2\rangle$ will each evolve independent of each other's existence, so for each possibility, it's as if the other possibility didn't exist.

So how often does this happen? After the initial "infection", the single valued particle in each universe will then evolve in a superposition of states again. So is this process happening at a very high frequency?

 

[PeroK]

So how often does this happen? After the initial "infection", the single valued particle in each universe will then evolve in a superposition of states again. So is this process happening at a very high frequency?

You might to read this.

http://physics.stackexchange.com/qu...lk-about-wave-functions-of-macroscopic-bodies

 

[jaydnul]

Maybe this is my question. Under what circumstances do we get this "infection" or "collapse"?

For instance, if two electrons are traveling towards each other they will eventually stop and repulse in the opposite direction. They never "collapse" to value, correct? Both of their possible positions and momentum are represented by amplitudes of their wavefunctions at any moment, which evolves in time. Essentially, they don't need to collapse to repulse.

But if a photon is traveling towards a hydrogen atom and is absorbed, then we can say the wavefunction did this "collapse" or "infection" at a specific point.

So does this notion of collapse only apply when the particle is absorbed and it's wavefunction dissapears?

 

[PeroK]

Maybe this is my question. Under what circumstances do we get this "infection" or "collapse"?

For instance, if two electrons are traveling towards each other they will eventually stop and repulse in the opposite direction. They never "collapse" to value, correct? Both of their possible positions and momentum are represented by amplitudes of their wavefunctions at any moment, which evolves in time. Essentially, they don't need to collapse to repulse.

But if a photon is traveling towards a hydrogen atom and is absorbed, then we can say the wavefunction did this "collapse" or "infection" at a specific point.

So does this notion of collapse only apply when the particle is absorbed and it's wavefunction dissapears?

A particle's wave function never disappears. The wave function of a particle contains all the information about its dynamic quantities: position, momentum, energy, angular momentum, spin.

You need to get a reliable source for an introduction to QM. This is not just about terminology, this is about the whole basis of the theory.

My other suggestion is to forget about QM and macroscopic objects. IMHO, it introduces a whole bunch of additional difficult questions, which can't really be addressed until you know the theory at the microscopic level in the first place.

 

[jaydnul]

It dissapears if the particle dissapears, ya?

 

[durant35]

Maybe this is my question. Under what circumstances do we get this "infection" or "collapse"?

For instance, if two electrons are traveling towards each other they will eventually stop and repulse in the opposite direction. They never "collapse" to value, correct? Both of their possible positions and momentum are represented by amplitudes of their wavefunctions at any moment, which evolves in time. Essentially, they don't need to collapse to repulse.

But if a photon is traveling towards a hydrogen atom and is absorbed, then we can say the wavefunction did this "collapse" or "infection" at a specific point.

So does this notion of collapse only apply when the particle is absorbed and it's wavefunction dissapears?

I think you're on a good way in your thinking but you are confusing yourself with some wrong ideas.

I believe that repulsion and apsorption aren't the key words here. The key words are "interaction" and "macroscopic". When a photon interacts with a physical object that is macroscopic in a sense that it has many particles/many degrees of freedom decoherence happens. It isn't fundamental if the photon is apsorbed or repulsed here (of course, if I'm wrong some of the senior PF members please correct).

The wavefunction of the photon doesn't disappear, as PeroK said - its components get decoupled and if you like the collapse interpretation all components (which you can regard as small, small waves in their own right) except one vanish and you get a measurement result which in reality is a small wave. There is still the wavefunction, but it gets reduced compared to its 'look' before the interaction.

 

[PeterDonis]

Particles have a wave function, and when measured, they choose one specific eigenvalue to "collapse" to.

Only if you are using a collapse interpretation of QM. There are interpretations, such as the many worlds interpretation, in which there is no collapse.

if two electrons are traveling towards each other they will eventually stop and repulse in the opposite direction

This is a classical model, not a quantum model. It makes no sense to ask questions about a classical model that are only meaningful for a quantum model.

 

[Mentz114]

''
There is a second level of mystery about macroscopic objects, though. In everyday experience, we never observe macroscopic objects to be in a superposition of macroscopically distinguishable states. A coin lying on a table is either heads or tails, and never in a superposition of the two. .

There is no mystery. Why would you expect macroscopic objects to be capable of super-position ? I might as well ask 'why can't I be in two places at the same time' ?
Mathematically, the thing we call the wave function becomes non-linear for macroscopic systems, so super-position is not predicted.

 

[stevendaryl]

There is no mystery. Why would you expect macroscopic objects to be capable of super-position ?

Because it follows from the Rules of Quantum Mechanics. If the state $|A\rangle$ evolves into the state $|A'\rangle$, and the state $|B\rangle$ evolves into the state $|B'\rangle$, then the state $\alpha |A\rangle + \beta |B\rangle$ evolves into the state $\alpha |A'\rangle + \beta |B'\rangle$.

Mathematically, the thing we call the wave function becomes non-linear for macroscopic systems, so super-position is not predicted.

That's not true. Quantum mechanics doesn't make a distinction between microscopic and macroscopic.

 

[stevendaryl]

So how often does this happen? After the initial "infection", the single valued particle in each universe will then evolve in a superposition of states again. So is this process happening at a very high frequency?

Wave function collapse (if it happens) gives you a pure state (uninfected by entanglement). Without collapse, I think things just keep getting more and more entangled. It's sort of like entropy increasing.

 

[stevendaryl]

Mathematically, the thing we call the wave function becomes non-linear for macroscopic systems, so super-position is not predicted.

I don't know what you are referring to here. Could you elaborate? In any case, the question "Why would you expect macroscopic objects to be capable of super-position ?" is answered by "It appears to be what QM predicts."

 

[Mentz114]

I don't know what you are referring to here. Could you elaborate? In any case, the question "Why would you expect macroscopic objects to be capable of super-position ?" is answered by "It appears to be what QM predicts."

I think it depends what you mean by super-position. If it is a statistical mixture, then macroscopic objects can be in such states.
For some reason I'm assuming you mean something else which is unwarranted.

 

[stevendaryl]

I think it depends what you mean by super-position. If it is a statistical mixture, then macroscopic objects can be in such states.

The issue (which I assume is what the title of this thread refers to) is how the classical world emerges from quantum mechanics. Why does the macroscopic world seem so definite--objects are here or there, but never in a superposition of two macroscopically distant locations---when the microscopic world involves superpositions. Saying "because macroscopic objects" can't be in superpositions is just begging the question, it's assuming the conclusion.

 

[Mentz114]

The issue (which I assume is what the title of this thread refers to) is how the classical world emerges from quantum mechanics. Why does the macroscopic world seem so definite--objects are here or there, but never in a superposition of two macroscopically distant locations---when the microscopic world involves superpositions. Saying "because macroscopic objects" can't be in superpositions is just begging the question, it's assuming the conclusion.

Actually I just said 'macroscopic objects can be in super-posed states'. My apparent volte-face is because I remembered what Dirac said about how to detect a super-position.

 

[stevendaryl]

Actually I just said 'macroscopic objects can be in super-posed states'. My apparent volte-face is because I remembered what Dirac said about how to detect a super-position.

I thought you were saying that they could only exist in statistical mixtures (which are different from superpositions). You said:

Mathematically, the thing we call the wave function becomes non-linear for macroscopic systems, so super-position is not predicted.

 

[Mentz114]

I thought you were saying that they could only exist in statistical mixtures (which are different from superpositions). You said:

As I suspected - this is where we differ. Super-positions are FAPP statistical mixtures. At least according to Dirac. I'll find the reference.

 

[stevendaryl]

As I suspected - this is where we differ. Super-positions are FAPP statistical mixtures. At least according to Dirac. I'll find the reference.

I wouldn't say it's where WE differ. I would say that it's where the @Mentz114 from post #25 differs from the @Mentz114 from post #33.

 

[Mentz114]

I wouldn't say it's where WE differ. I would say that it's where the @Mentz114 from post #25 differs from the @Mentz114 from post #33.

I'm not denying that - but you were wondering why macroscopic objects didn't make super-positions, say between registering 'on' and 'off'.
They would pass the test. I refer to Dirac's Principles ... page 13, paragraph 2, especially the italicised bit at the end.